Question

Обчисліть значення виразу $\frac{(\sqrt[4]{3}- \sqrt[4]{2)}(\sqrt[4]{3}+\sqrt[4]{2})(\sqrt{3}+\sqrt{2} ) }{\sqrt[3]{27+1} }$

Answer 1

Решение:

$\frac{(\sqrt[4]{3}-\sqrt[4]{2})(\sqrt[4]{3}+\sqrt[4]{2})(\sqrt{3}+\sqrt{2})}{\sqrt[3]{27}+1}=\frac{((\sqrt[4]{3})^{2}-(\sqrt[4]{2})^{2})(\sqrt{3}+\sqrt{2})}{3+1}=\frac{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}{4}=\frac{((\sqrt{3})^{2}-(\sqrt{2})^{2})}{4}=\frac{3-2}{4}=\frac{1}{4}=0,25$

Ответ: 0,25

$DK954$